A multiplicative product of distributions and a global formulation of the confined Schrodinger equation

Details A multiplicative product of distributions and a global formulation of the confined Schrodinger equation A multiplicative product of distributions and a global formulation of the confined Schrodinger equation

2008-12-03

arxiv.org/abs/0812.0638v1

Journal of Generalized Lie Theory and Applications, 2 (2008), No.3, 137

Mathematics

Functional Analysis

5 pages, no figures. Presented by N.C. Dias at the 3rd Baltic-Nordic Workshop "Algebra, Geometry, and Mathematical Physics", G

Scientific paper

A concise derivation of a new multiplicative product of Schwartz distributions is presented. The new product $\star$ is defined in the vector space ${\cal A}$ of piecewise smooth functions on $\bkR$ and all their (distributional) derivatives; it is associative, satisfies the Leibnitz rule and reproduces the usual product of functions for regular distributions. The algebra $({\cal A},+,\star)$ yields a sufficiently general setting to address some interesting problems. As an application we consider the problem of deriving a global formulation for quantum confined systems.

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